INVARIANTS OF LINKS AND CRITICAL POINTS OF THE CHERN-SIMON PATH INTEGRALS

Abstract

A method is given for evaluating the functional integrals of Chern-Simon field theories to first nontrivial order. The basis of this method is a background independent regularization which allows the factors associated with twists of the framing of loops to be computed. To first order, Witten’s result connecting the Jones polynomial to expectation values of the Chern-Simon theory is reproduced. Additionally, a method for constructing solutions to the classical field equations of the theory is described, and it is shown that a static solution to Einstein’s equations (in Ashtekar’s form) may be associated with every such solution.